FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2186201478> ?p ?o ?g. }

• W2186201478 abstract "The problem of choosing efficient algorithms and good admissible orders for computing Grobner bases in noncommutative algebras is considered. Grobner bases are an important tool that make many problems in polynomial algebra computationally tractable. However, the computation of Grobner bases is expensive, and in noncommutative algebras is not guaranteed to terminate. The algorithm, together with the order used to determine the leading term of each polynomial, are known to affect the cost of the computation, and are the focus of this thesis.A Grobner basis is a set of polynomials computed, using Buchberger's algorithm, from another set of polynomials. The noncommutative form of Buchberger's algorithm repeatedly constructs a new polynomial from a triple, which is a pair of polynomials whose leading terms overlap and form a nontrivial common multiple. The algorithm leaves a number of details underspecified, and can be altered to improve its behavior. A significant improvement is the development of a dynamic dictionary matching approach that efficiently solves the pattern matching problems of noncommutative Grobner basis computations. Three algorithmic alternatives are considered: the strategy for selecting triples (selection), the strategy for removing triples from consideration (triple elimination), and the approach to keeping the set interreduced (set reduction).Experiments show that the selection strategy is generally more significant than the other techniques, with the best strategy being the one that chooses the triple with the shortest common multiple. The best triple elimination strategy ignoring resource constraints is the Gebauer-Moller strategy. However, another strategy is defined that can perform as well as the Gebauer-Moller strategy in less space.The experiments also show that the admissible order used to determine the leading term of a polynomial is more significant than the algorithm. Experiments indicate that the choice of order is dependent on the input set of polynomials, but also suggest that the length lexicographic order is a good choice for many problems. A more practical approach to choosing an order may be to develop heuristics that attempt to find an order that minimizes the number of overlaps considered during the computation." @default.
• W2186201478 created "2016-06-24" @default.
• W2186201478 creator A5080434535 @default.
• W2186201478 date "1998-03-17" @default.
• W2186201478 modified "2023-10-18" @default.
• W2186201478 title "Algorithms and orders for finding noncommutative Grobner bases" @default.
• W2186201478 cites W101469639 @default.
• W2186201478 cites W1495940585 @default.
• W2186201478 cites W1496412704 @default.
• W2186201478 cites W1503860275 @default.
• W2186201478 cites W1516979491 @default.
• W2186201478 cites W1542689491 @default.
• W2186201478 cites W1635682819 @default.
• W2186201478 cites W1678926756 @default.
• W2186201478 cites W1968936725 @default.
• W2186201478 cites W1971551964 @default.
• W2186201478 cites W1980349404 @default.
• W2186201478 cites W1982024542 @default.
• W2186201478 cites W1984553083 @default.
• W2186201478 cites W1987599384 @default.
• W2186201478 cites W1993974377 @default.
• W2186201478 cites W2016313336 @default.
• W2186201478 cites W2020759317 @default.
• W2186201478 cites W2023007275 @default.
• W2186201478 cites W2031501281 @default.
• W2186201478 cites W2039225816 @default.
• W2186201478 cites W2041611195 @default.
• W2186201478 cites W2046359229 @default.
• W2186201478 cites W2063556310 @default.
• W2186201478 cites W2063685460 @default.
• W2186201478 cites W2069738583 @default.
• W2186201478 cites W2077725083 @default.
• W2186201478 cites W2080111120 @default.
• W2186201478 cites W2093144183 @default.
• W2186201478 cites W2093397547 @default.
• W2186201478 cites W2099964107 @default.
• W2186201478 cites W2109851385 @default.
• W2186201478 cites W2121252285 @default.
• W2186201478 cites W2137416248 @default.
• W2186201478 cites W2138135391 @default.
• W2186201478 cites W2507006525 @default.
• W2186201478 cites W2611708922 @default.
• W2186201478 cites W2912818154 @default.
• W2186201478 cites W98590612 @default.
• W2186201478 hasPublicationYear "1998" @default.
• W2186201478 type Work @default.
• W2186201478 sameAs 2186201478 @default.
• W2186201478 citedByCount "3" @default.
• W2186201478 countsByYear W21862014782013 @default.
• W2186201478 crossrefType "dissertation" @default.
• W2186201478 hasAuthorship W2186201478A5080434535 @default.
• W2186201478 hasConcept C105795698 @default.
• W2186201478 hasConcept C11413529 @default.
• W2186201478 hasConcept C134306372 @default.
• W2186201478 hasConcept C136119220 @default.
• W2186201478 hasConcept C154945302 @default.
• W2186201478 hasConcept C165064840 @default.
• W2186201478 hasConcept C177264268 @default.
• W2186201478 hasConcept C198082693 @default.
• W2186201478 hasConcept C199360897 @default.
• W2186201478 hasConcept C202444582 @default.
• W2186201478 hasConcept C33923547 @default.
• W2186201478 hasConcept C41008148 @default.
• W2186201478 hasConcept C45374587 @default.
• W2186201478 hasConcept C68797384 @default.
• W2186201478 hasConcept C81917197 @default.
• W2186201478 hasConcept C90119067 @default.
• W2186201478 hasConceptScore W2186201478C105795698 @default.
• W2186201478 hasConceptScore W2186201478C11413529 @default.
• W2186201478 hasConceptScore W2186201478C134306372 @default.
• W2186201478 hasConceptScore W2186201478C136119220 @default.
• W2186201478 hasConceptScore W2186201478C154945302 @default.
• W2186201478 hasConceptScore W2186201478C165064840 @default.
• W2186201478 hasConceptScore W2186201478C177264268 @default.
• W2186201478 hasConceptScore W2186201478C198082693 @default.
• W2186201478 hasConceptScore W2186201478C199360897 @default.
• W2186201478 hasConceptScore W2186201478C202444582 @default.
• W2186201478 hasConceptScore W2186201478C33923547 @default.
• W2186201478 hasConceptScore W2186201478C41008148 @default.
• W2186201478 hasConceptScore W2186201478C45374587 @default.
• W2186201478 hasConceptScore W2186201478C68797384 @default.
• W2186201478 hasConceptScore W2186201478C81917197 @default.
• W2186201478 hasConceptScore W2186201478C90119067 @default.
• W2186201478 hasLocation W21862014781 @default.
• W2186201478 hasOpenAccess W2186201478 @default.
• W2186201478 hasPrimaryLocation W21862014781 @default.
• W2186201478 hasRelatedWork W100926944 @default.
• W2186201478 hasRelatedWork W1565266802 @default.
• W2186201478 hasRelatedWork W1588380139 @default.
• W2186201478 hasRelatedWork W1867103688 @default.
• W2186201478 hasRelatedWork W1969511582 @default.
• W2186201478 hasRelatedWork W2048068744 @default.
• W2186201478 hasRelatedWork W2056432814 @default.
• W2186201478 hasRelatedWork W2074771195 @default.
• W2186201478 hasRelatedWork W2096891389 @default.
• W2186201478 hasRelatedWork W22024973 @default.
• W2186201478 hasRelatedWork W2402945515 @default.
• W2186201478 hasRelatedWork W2475880652 @default.
• W2186201478 hasRelatedWork W2576511634 @default.
• W2186201478 hasRelatedWork W2759544031 @default.

• next